The White House "looks forward to continuing to work with both the House and the Senate to increase certainty and stability for the economy," the statement concluded.
However, some conservative House Republicans oppose Boehner's debt ceiling measure, setting up a possible repeat of previous votes in which the speaker failed to get enough support from his GOP conference to push through a bill.
"I think it's a terrible idea," Rep. Tom McClintock, R-California, told Fox Business Network on Monday, arguing the plan "gives the most spendthrift administration in this country's history literally an open credit card to borrow as much as they can."
Rep. Louie Gohmert, R-Texas, also disagreed with giving up the leverage of the debt ceiling without any guaranteed spending cuts in return.
"At some point, we have got to use the leverage we have to bring this spending down and to actually make the president do what he said in his speech," Gohmert told FBN.
In addition, Gohmert complained that Boehner's plan essentially gives the "millionaires club" in the Senate the power to determine whether he and other House members who need their congressional salaries will get paid.
At the White House, spokesman Jay Carney called the House GOP plan "a welcome thing" and rejected accusations that Obama's address Monday amounted to liberal ideology.
"He focuses on the fact that we are Americans first, and I hardly thing the pursuit of equal rights, pursuit of comprehensive immigration reform, pursuit of sensible policies that deal with climate change and enhance our energy independence are ideological," Carney said Tuesday.
In the Senate, Majority Leader Harry Reid outlined an agenda that closely conformed to the priorities of the president's inaugural address the day before.
"The last Congress was too often characterized by sharp political divides -- divides that hampered efforts to foster success for all Americans," the Nevada Democrat said, telling his colleagues that "it is possible to hold fast to your principles while making the compromises necessary to move our country forward."
At the same time, Reid said Senate Democrats "will stand strong -- strong -- for the standard of balance, and we will remain resolute -- resolute -- in the pursuit of fairness for all Americans, regardless of where they were born or the color of their skin, regardless of the size of their bank accounts, regardless of their religion or their sexual orientation."
McConnell also called for compromise but said it was Democrats who must be willing to meet in the middle.
"Over the past four years, while the president focused on re-election and too many Senate Democrats focused on avoiding tough decisions, the debt grew by more than $6 trillion," McConnell said. "In short, Democrats have put off all the hard stuff until now. And our problems have only gotten worse. But that was the first term."
Saying "a lot of Democrats are afraid of a process that exposes their priorities, particularly on spending and debt," McConnell made clear that Republicans reject any further increases in tax revenue after the fiscal cliff deal at the end of the last Congress that raised rates on top income earners.
"Since the revenue question has been settled," he said, "I'm sure the American people are eager to see what other ideas Democrats might have to bring down our ruinous deficits."